An urn contains balls of different colors; there are balls of color. Balls are selected at random from the urn, one by one, without replacement, until among the selected balls balls of the same color appear. Find the greatest number of selections.
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An urn contains balls of $k$ different colors; there are $n_i$ balls of $i-th$ color. Balls are selected at random from the urn, one by one, without replacement, until among the selected balls $m$ balls of the same color appear. Find the greatest number of selections.
Izvor: Međunarodna matematička olimpijada, shortlist 1967
Školjka 
different colors; there are 
balls of 
color. Balls are selected at random from the urn, one by one, without replacement, until among the selected balls 
balls of the same color appear. Find the greatest number of selections.